Modified Quasichemical Model Research Articles

Thermodynamic Evaluation and Optimization of the SrO-MgO, SrO-SiO2 and SrO-MgO-SiO2 Systems

The SrO-MgO and SrO-SiO2 systems have been critically evaluated based upon available phase equilibrium and thermodynamic data, and optimized model parameters have been obtained giving the Gibbs energies of all phases as functions of temperature and composition. The liquid solution has been modeled with the Modified Quasichemical Model to account for short-range-ordering. The results have been combined with those of previous optimizations of the MgO-SiO2 system in the optimization of the SrO-MgO-SiO2 system.

Experimental and thermodynamic study of the Mg-Sn-Ca-Sr quaternary system: Part I-Mg-Sn-Ca ternary system

Four key samples of the Mg-Ca-Sn ternary system in the Mg-rich region at 415 and 350°C have been determined using the Scanning Electron Microscopy (SEM) equipped with Energy Dispersive X-Ray Spectrometry (EDS). The existence of the CaMgSn ternary compound was confirmed in these two isothermal sections. Thermodynamic optimizations of the Ca-Sn binary system and Mg-Ca-Sn ternary system were carried out using the CALPHAD (Calculation of Phase Diagrams) technique. The Modified Quasichemical Model (MQM) was used for the liquid solution which exhibits a high degree of short-range ordering behavior in the liquid solution. The solid phases are modeled with the Compound Energy Formalism (CEF). Finally, a self-consistent thermodynamic database of Mg-Ca-Sn ternary system has been constructed in the present work, which would provide an efficient and convenient way to study and develop the new Mg-Sn based alloys.

Thermodynamic assessments of the Cr-Si and Al-Cr-Si systems

Abstract Thermodynamic assessments for the Cr-Si and Al-Cr-Si systems were conducted on the basis of the critically evaluated thermodynamic and phase diagram data available in the literature. The Modified Quasi-chemical Model (MQM) was utilized to model the Gibbs energy of the liquid phase and the Compound Energy Formalism (CEF) was used to model the solid phases. Comprehensive comparison between the model-predicted and the experimentally measured phase diagram and thermodynamic property data indicates that the optimized thermodynamic descriptions for the Cr-Si and Al-Cr-Si systems are reliable. Accurate thermodynamic descriptions obtained in the present work in the form of a set of Gibbs energies of all the solid and liquid phases can be used to calculate the phase equilibria and thermodynamic properties in the Al-Cr-Si system at any composition and temperature. As the application of the present thermodynamic study, the solubility limit of Cr in the Al-Si alloy was calculated.

Thermodynamic modeling of the quaternary Al-Cu-Mg-Si system

Based on the critically evaluated thermodynamic and phase diagram information available in the literature, thermodynamic modeling of the Cu-Mg, Al-Cu-Mg, Al-Cu-Si, and Cu-Mg-Si systems were conducted using the CALPHAD (CALculation of PHAse Diagrams) technique. The liquid phase was described using the Modified Quasi-chemical Model (MQM), and the solid solution phases were modeled with the Compound Energy Formalism (CEF). Based on the newly obtained and the previously published thermodynamic descriptions of the subsystems, a set of self-consistent thermodynamic description for the Al-Cu-Mg-Si quaternary system was constructed. Comprehensive comparison between the calculated and measured thermodynamic and phase diagram information indicated that most of the reliable experimental data in the quaternary system can be satisfactorily reproduced by the presently obtained thermodynamic description. The optimized thermodynamic parameters can be used for the calculations of the phase diagram and thermodynamic properties of any composition and temperature range in the Al rich Al-Cu-Mg-Si quaternary system.

Thermodynamic modeling of the Cu-Fe-Cr and Cu-Fe-Mn systems

All the thermodynamic and phase diagram information available in the literature on the Cu-Cr system, Cu-Fe-Cr system, and Cu-Fe-Mn system were critically evaluated and used in the thermodynamic optimization to obtain a set of consistent thermodynamic model parameters for the systems. The liquid solutions for the Cu-Cr, Cu-Mn, Fe-Cr, Cu-Fe-Cr, and Cu-Fe-Mn systems were described using the Modified Quasichemical Model (MQM) with pair approximation. The solid solution phases were modeled using the Bragg-Williams random mixing model. Accurate reproduction of all the reliable phase diagram and thermodynamic property data indicates the high reliability of the present thermodynamic optimizations.

Critical evaluation and thermodynamic optimization of the Li-O, and Li2O-SiO2 systems

A critical evaluation and thermodynamic optimization of all available experimental data of the Li-O and Li2O-SiO2 systems were performed to obtain one set of consistent Gibbs energy functions for all phases in the systems. The obtained Gibbs energy functions can reproduce all available and reliable experimental data from 298K to above liquidus temperatures at one atm total pressure. It is the first time, to the best of our knowledge that the Gibbs energy of stoichiometric phases like Li2O, Li4SiO4, Li2SiO3, and Li2Si2O5 was comprehensively evaluated and optimized. The liquid oxide solution was modeled using the Modified Quasichemical Model to describe its thermodynamic behavior accurately considering the short range ordering. Discrepancies observed in the metastable liquid immiscibility and the liquidus in the SiO2-rich region of the Li2O-SiO2 system was resolved. The phase diagram and thermodynamic data of all the solid and liquid phases were well reproduced within experimental error limits.

Thermodynamic Modeling of the Al-Cr-Mn Ternary System

The phase diagram information available in the literature on the Al-Cr-Mn system was comprehensively evaluated and optimized for the first time to obtain a set of Gibbs energies of all the solid and liquid phases in the Al-Cr-Mn system. The Modified Quasi-chemical Model (MQM) was utilized to describe the Gibbs energy of the liquid phase of the Al-Cr-Mn system. The Compound Energy Formalism (CEF) was used to model the solid solution phases. A revision of the Al-Mn system was simultaneously conducted to consider the γ_H (Al8Mn5) phase. The liquid Cr-Mn phase was also remodeled using the Modified Quasi-chemical Model (MQM) to obtain a consistent description of the ternary Al-Cr-Mn liquid phase. Accurate description of the phase diagram of the entire Al-Cr-Mn system was obtained from the thermodynamic models with optimized parameters in the present study, and the model parameters can be used to predict the thermodynamic properties of the ternary system.

Thermodynamic Modeling of Fe–C–S Ternary System

A CALPHAD type thermodynamic modeling of the Fe–C–S system was carried out, in particular, in order to provide accurate description of activity-composition relationship of Fe–C–S liquid phase. The liquid may be used as a solvent of ferrous scrap recycling. All available and reliable experimental data including phase equilibria and activity of S in the liquid Fe–C–S were analyzed, and a self-consistent set of Gibbs energy equations for the stable phases were obtained. In addition to the Gibbs energy equations, interaction parameters between S and C in the liquid were additionally estimated as functions of temperature:which were derived from the optimized Gibbs energy of the liquid phase using the Modified Quasichemical Model in the pair approximation. Moreover, the present thermodynamic modeling can be used to calculate various phase diagrams in the Fe–C–S system, and can be further extended in order to develop a multicomponent thermodynamic database.

Critical evaluation and thermodynamic optimization of the CaO-ZrO2 and SiO2-ZrO2 systems

Thermodynamic optimizations of unary ZrO2, binary CaO-ZrO2 and SiO2-ZrO2 systems were carried out based on the critical evaluation of all available thermodynamic properties and phase diagram data in literature. Liquid phase was described by using the Modified Quasichemical Model considering the short range ordering, and solid solutions were described considering their defect structures. The discrepancies among experimental phase diagram data and possible errors in the existing thermodynamic data were identified and the most reliable thermodynamic descriptions of the systems were obtained.

A density model based on the Modified Quasichemical Model and applied to the (LiCl+KCl+CsCl) liquid

Differential scanning calorimetry analysis of the various compositions in the (LiCl+CsCl) and (LiCl+KCl+CsCl) systems have been performed, and the composition of 55.5:19.5:25mol% and 263°C were considered as a eutectic point in the (LiCl+KCl+CsCl) ternary system. A careful evaluation and optimization of our measured phase diagram data and all the other available experimental data for the (LiCl+CsCl) and (LiCl+KCl+CsCl) systems were performed to obtain optimized model parameters for all solid and liquid phases. A thermodynamic data set has been formed and may be used to calculate phase equilibrium and all thermodynamic properties in the (LiCl+KCl+CsCl) ternary system. A density model based on the Modified Quasichemical Model has been employed to evaluate all available density data of the (LiCl+KCl), (KCl+CsCl), (LiCl+CsCl) and (LiCl+KCl+CsCl) melts, and optimized parameters for the density model generated a useful database that can be used to complete a prediction for the density of all liquid phases.

Thermodynamic assessment of the Nd2O3-CaO-SiO2 ternary system

In order to enable efficient recycling of rare earth metals through high temperature processes, the phase relations in rare earth oxide containing slags need to be understood. A thermodynamic description of the CaO-SiO2-Nd2O3 ternary system and its Nd-containing binary subsystems was, therefore, constructed in this study, based on existing phase diagram and thermodynamic data. The Gibbs energy of the liquid oxides in the CaO-SiO2-Nd2O3 system was modeled using the Modified Quasichemical Model. The solid phases Ca2-2xNd2xSiO4Ox, Ca3-3xNd2xSiO5, and Ca2+10xNd8-8x(SiO4)6O2-2x were modeled with polynomial expansions of the excess Gibbs energy. The optimized phase diagram of the CaO-SiO2-Nd2O3 system is in good agreement with the experimental data.

Critical evaluation and thermodynamic optimization of the Sn–RE systems: Part I. Sn–RE system (RE=La, Ce, Pr, Nd and Sm)

A critical evaluation and optimization of all available phase diagrams and thermodynamic data of the binary Sn–RE (RE=La, Ce, Pr, Nd and Sm) systems was conducted to obtain reliable thermodynamic functions of all the phases in the systems. In particular, the thermodynamic properties of liquid phase were described using the Modified Quasichemical Model which takes into account the short range ordering of solution. In the thermodynamic optimization, a systematic analysis involving the similarity and periodicity in the phase diagrams and the thermodynamic properties observed in the lanthanide series was applied to resolve inconsistencies in the available experimental data and to estimate the unknown thermodynamic properties and phase equilibria data.

Critical evaluation and thermodynamic optimization of the Sn–RE systems: Part II. Sn–RE system (RE=Gd, Tb, Dy, Ho, Er, Tm, Lu and Y)

A critical evaluation and optimization of all available phase diagrams and thermodynamic data of the binary Sn–RE (RE=Gd, Tb, Dy, Ho, Er, Tm, Lu and Y) systems was conducted to obtain reliable thermodynamic functions of all the phases in the system. In particular, the thermodynamic properties of liquid phase were described using the Modified Quasichemical Model which takes into account the short range ordering of solution. The systematic analysis and the uncertainties in the Sn–RE systems were discussed.

Critical evaluation and thermodynamic optimization of the Na2O–FeO–Fe2O3–Al2O3–SiO2 system

A critical assessment and thermodynamic optimization of phase diagrams and thermodynamic properties of the entire Na2O–FeO–Fe2O3–Al2O3–SiO2 system were carried out at 1atm total pressure. A set of optimized model parameters obtained for all phases present in this system reproduces available and reliable thermodynamic property and phase equilibrium data within experimental error limits from 298K to above liquidus temperatures for all compositions and oxygen partial pressures from metallic Fe saturation to 1atm. The Gibbs energy of liquid solution was described based on the Modified Quasichemical Model considering the possible formation of NaAlO2 and NaFeO2 associates in the liquid state. The solid solutions wüstite, spinel, feldspar, nepheline, carnegieite, mullite, corundum, clino-pyroxene, meta-oxides and Na-β″-alumina were treated within the framework of Compound Energy Formalism. The database of model parameters can be used to calculate any thermodynamic property and phase diagram section of the present system.

Aluminum Deoxidation Equilibria in Liquid Iron: Part III—Experiments and Thermodynamic Modeling of the Fe-Mn-Al-O System

Deoxidation equilibria in high-Mn- and high-Al-alloyed liquid steels were studied over the entire Fe-Mn-Al composition range by both experiments and thermodynamic modeling. Effect of Mn on the Al deoxidation equilibria in liquid iron was measured by the different experimental techniques depending on the Al content. In order to confirm the reproducibility of the experimental results, the deoxidation experiments were carried out reversibly from high oxygen state by addition of Al as a deoxidizer, and from low oxygen state by addition of Fe2O3 or MnO as an oxygen source. For the Al-rich side, CaO flux was added on top of liquid iron in order to remove suspended Al2O3 inclusions in the melt. Based on the present experimental result and available critically evaluated literature data, the Al deoxidation equilibria in Fe-Mn-Al-O liquid alloy were thermodynamically modeled. The Modified Quasichemical Model was used in order to take into account a strong short-range ordering of atoms in molten state. Deoxidation equilibria and inclusion stability diagram for entire Fe-Mn-Al melt were successfully reproduced by the present model.

Thermodynamic analysis of dehydrogenation path of Mg–Al–Li–Na alloys

A thermodynamic study on the Mg–Al–Li–Na–H system is conducted in this work in order to investigate its hydrogen storage properties. For that purpose, a thermodynamic database is constructed using the CALPHAD technique. In this work, Li is added to the previously studied Mg–Al–Na–H system and the related binaries (Li–Mg, Li–Na) and ternaries (Al–Li–Mg, Al–Li–H, Li–Mg–H) are reassessed using the Compound Energy Formalism (CEF) for the terminal solid solutions and the Modified Quasichemical Model (MQM) for the liquid phase. The quaternary hydride Na2LiAlH6 is assessed for the first time. The constructed database is used to calculate de/re-hydrogenation reaction pathways of MgH2–LiAlH4/Li3AlH6 composites in a wide temperature and pressure ranges. The results are analyzed and compared with the experimental data to better understand and predict the reaction mechanisms. It is shown that Al resulted from the decomposition of LiAlH4/Li3AlH6 hydrides destabilizes MgH2 by the formation of Mg–Al phases: β and γ, and that LiH does not contribute to these reactions. Only negligible amounts of hydrogen are released from LiH because of the limited solubility of Li (from LiH) in Mg at high temperatures. It is concluded that MgH2–Li3AlH6 system has better reversibility than MgH2–LiAlH4 system and promising compositions (e.g. 37.09mol% and 53.65mol% MgH2 contents) are predicted. Also, a new destabilization reaction is predicted in the system. The MgH2 and Na2LiAlH6 hydrides destabilize mutually at 308.4K (35.25°C) and 1bar because of the formation of MgNaH3. However, the hydrogen capacity is reduced. It is concluded that Na considerably reduces the hydrogen storage potential of the system.

ChemInform Abstract: Thermodynamic Modeling of the Fe—Mn—C and the Fe—Mn—Al Systems Using the Modified Quasichemical Model for Liquid Phase

AbstractReview: 88 refs.

Erratum to: Thermodynamic Modeling of the Fe-Mn-C and the Fe-Mn-Al Systems Using the Modified Quasichemical Model for Liquid Phase

Erratum to: Thermodynamic Modeling of the Fe-Mn-C and the Fe-Mn-Al Systems Using the Modified Quasichemical Model for Liquid Phase

Thermodynamic evaluation and optimization of the (KF + YF3), (KCl + YCl3) and (YF3 + YbF3) binary systems

A careful evaluation and optimization of all available phase equilibrium and thermodynamic data for the (KF+YF3), (KCl+YCl3) and (YF3+YbF3) binary systems was performed to obtain optimized model parameters for all solid and liquid phases. After the discussion of four different optimization strategies, the Modified Quasichemical Model in the pair approximation with two short-range ordering compositions near xYX3=0.25 and 0.4 (X=Cl,F) proved to be a suitable method to model the molten salt phase of the (KX+YX3) binary systems. The liquid phase of the (YF3+YbF3) binary system was considered to be ideal. All thermodynamic data (phase diagram, enthalpy of mixing, activity) that are available for the three binary systems are reproduced within experimental error limits.

Thermodynamics of Nitrogen in Fe-Mn-Al-Si-C Alloy Melts

Thermodynamic behavior of nitrogen in the entire range of the Fe-Mn-Al-Si-C liquid solution was modeled based on the critical evaluation and optimization of all available experimental data. The Gibbs energy of liquid solution was described using the Modified Quasichemical Model (MQM) in the pair approximation, instead of classical Wagner Interaction Parameter Formalism, to consider the strong interactions between species in liquid state. In particular, the dissolution behavior of N and formation of AlN in the entire ternary and higher order liquids were accurately predicted from the MQM only with binary model parameters of N.